STAT 5050 Homework 4
1. To examine whether certain regions of brains of people with schizophrenia differ from those
without the condition, 15 pairs of monozygotic (so-called “identical”) twins were studied; in
each pair, one suffered from schizophrenia. Left hippocampus volumes were measured
(postmortem) for each subject. What is the magnitude of the average difference in volume of
the left hippocampus between the unaffected and affected individuals? Can the observed
differences be attributed to mere chance, or are they statistically significant? Data are in the
dataset hippocampus. The two columns are labeled as “affected” and “unaffected” (by
schizophrenia). Be sure to consider validity of formal statistical tools you use.
The hippocampus is a part of the brain located in the
medial temporal lobe (humans and other mammals
have two hippocampi, one in each side of the brain).
It forms a part of the limbic system and plays a part in
memory and spatial navigation. The name derives
from its curved shape in coronal sections of the brain,
which resembles a seahorse (Greek: hippos = horse,
kampi = curve).
2. In a study to determine reasons for greater honey productivity in honey bees (compared to
larger bumblebees), a researcher measured the time (in seconds) spend at flowers for a sample
of honey bees and a sample of bumblebees. Do honey bees spend more time at a flower than
bumblebees? Be sure to consider validity of formal statistical tools you use.
The data set is called Working Bees.
3. In a study attempting to predict abundance of prey items on the menu of Siberian tigers (more
properly “Amur” tigers, after the river drainage that encompasses much of their territory),
researchers recorded track encounter rates (number per kilometer) along the border of a 10km
by 10km square. Then they counted the number of animals inside the square (yielding a density
estimate). They wish to use the track encounter rate as the predictor in a regression model with
density as the response. Data are in Tiger prey abundance.
a. For each of the 5 assumptions for regression explain whether you believe the
assumption is violated or not (and why).
b. Assuming simple linear regression is appropriate test whether track encounter rate is a
good predictor for density.
4. Is lifespan of an electrical part affected by the voltage under which it works? Time (in minutes) is
the response; pre-set voltage rates the predictor. Data are in Voltage.
a. For each of the 5 assumptions for regression explain whether you believe the
assumption is violated or not (and why).
b. Assuming simple linear regression is appropriate test whether operating voltage is a
good predictor for lifespan.